Factorisation

• The reverse process to expanding is called factorisation. In this case we are given an expression which is a sum of terms and we convert it to a product of two or more terms.
• Expressions may be factorised by removing factors common to two or more terms and then by grouping and if necessary regrouping.
• For example: \(
  \newcommand{\eqncomment}[2]{\small{\text{ #2}} } 
  \newcommand{\ceqns}{\begin{array}{rcll}}
  \newcommand{\ceqne}{\end{array}}
  \)
  \[
  \ceqns
  && 3x+3x^2 \\
  &=& 3\times x+2x\times x & \eqncomment{0.4}{where \(x\) is the common factor} \\
  &=& x(3+2x)
  \ceqne
  \]
• Another example of factorising:

\begin{eqnarray}
2x^{3} +4x^{2}+6x = 2x(x^{2}+2x+3)
\end{eqnarray}
where \(2x\) is the common factor.